TY - JOUR

T1 - Models for the extremes of Markov chains.

AU - Borot, Paola

AU - Tawn, Jonathan A.

PY - 1998/12

Y1 - 1998/12

N2 - The modelling of extremes of a time series has progressed from the assumption of independent observations to more realistic forms of temporal dependence. In this paper, we focus on Markov chains, deriving a class of models for their joint tail which allows the degree of clustering of extremes to decrease at high levels, overcoming a key Limitation in current methodologies. Theoretical aspects of the model are examined and a simulation algorithm is developed through which the stochastic properties of summaries of the extremal txhaviour of the chain are evaluated. The approach is illustrated through a simulation study of extremal events of Gaussian autoregressive processes and an application to temperature data.

AB - The modelling of extremes of a time series has progressed from the assumption of independent observations to more realistic forms of temporal dependence. In this paper, we focus on Markov chains, deriving a class of models for their joint tail which allows the degree of clustering of extremes to decrease at high levels, overcoming a key Limitation in current methodologies. Theoretical aspects of the model are examined and a simulation algorithm is developed through which the stochastic properties of summaries of the extremal txhaviour of the chain are evaluated. The approach is illustrated through a simulation study of extremal events of Gaussian autoregressive processes and an application to temperature data.

KW - Asymptotic independence • Bivariate extreme value distribution • Extremal index • Extreme value theory • Gaussian process • Markov chain

U2 - 10.1093/biomet/85.4.851

DO - 10.1093/biomet/85.4.851

M3 - Journal article

VL - 85

SP - 851

EP - 867

JO - Biometrika

JF - Biometrika

SN - 1464-3510

IS - 4

ER -